The U.S. Court of Appeals for the District of Columbia Circuit, Kavanaugh's former court, received a number of complaints relating to his testimony before the Senate. Judge Karen LeCraft Henderson reviewed the complaints after former Supreme Court nominee Merrick Garland recused himself. Henderson determined that some concerns were insubstantial, but more than a dozen warranted further investigation. She then sent them to Roberts.

In a letter sent on Wednesday, Roberts, who was appointed by President George W. Bush, noted he was transferring the complaints to the 10th Circuit Court's chief judge, Timothy Tymkovich. The relocation to another circuit was motivated by "concern that local disposition may weaken public confidence in the process," CNN reported.

The chief justice asked for the exercise of powers "of a judicial council with respect to the identified complaints and any pending or new complaints relating to the same subject matter." The concerns do not relate to Kavanaugh's actions as a judge.

Tymkovich, who was on President Donald Trump's short list for the Supreme Court, can deal with the complaints himself, nullify them or appoint a special committee to further investigate, according to Forbes.

"The situation is unique in that never before has a Supreme Court appointee joined the court at a time when a fellow judge has concluded that misconduct claims against that appointee warrant review and when a former Supreme Court Justice has concluded that the appointee's behavior was disqualifying," Forbes reported. "Technically, Supreme Court justices are not subject to the misconduct rules governing these claims."

President Donald Trump puts his hand on Supreme Court Justice Brett Kavanaugh's shoulder during a ceremonial swearing in in the East Room of the White House. Chip Somodevilla/Getty Images

Kavanaugh openly displayed anger and irritation during his exchanges with lawmakers last month. He portrayed himself as a victim of a broader political discussion, saying "this whole two-week effort has been a calculated and orchestrated political hit fueled with apparent pent-up anger about President Trump and the 2016 election, fear that has been unfairly stoked about my judicial record. Revenge on behalf of the Clintons and millions of dollars in money from outside left-wing opposition groups. This is a circus."

In two remarkable interactions, Kavanaugh interrupted Senator Dianne Feinstein and responded "I don't know, have you?" to Senator Amy Klobuchar, who asked the judge if he'd ever consumed so much alcohol he couldn't remember what happened.

"I was stunned," Klobuchar said of the exchange. "One guy has said that he gets belligerent. So I was asking him about it, and I was stunned where instead of answering it he turned it on me. He did apologize very clearly after the break, which I appreciated. But the point is we still don't really have answers to those questions."

Kavanaugh's demeanor while testifying led to other vocal opposition. Retired Supreme Court Justice John Paul Stevens said Kavanaugh's conduct should bar him from serving on the nation's highest court.

More than 2,400 law professors said in a New York Times opinion piece wrote that the newest Supreme Court judge "displayed a lack of judicial temperament that would be disqualifying for any court" while testifying before the Senate Judiciary Committee. Kavanaugh personally expressed regret for some of his testimony in a Wall Street Journal editorial written last week. "I was very emotional last Thursday, more so than I have ever been. I might have been too emotional at times. I know that my tone was sharp, and I said a few things I should not have said," he wrote.

Update: This story has been updated to include further comments from Amy Klobuchar and John Paul Stevens.